Nicolas Tagliafico's first-half own goal was the difference between the sides in an end-to-end Group D game short on midfield control at Johan Cruyff Arena.
Starting life without injured talismanic centre-back Virgil van Dijk in the Dutch capital, the visitors could have done without the early mix-up between Adrian and Joe Gomez that suggested their defensive organisation is set to suffer.
Davy Klaassen struck the post but that was as close as Ajax came to salvaging a point.
Hearts had been in Liverpool mouths again when Adrian's attempt to launch the ball forward was closed down, leading to a headed chance for Lisandro Martinez that needed saving.
Another well-worked Ajax move then ended in Quincy Promes being picked out at close range, but he somehow failed to beat Adrian when a goal looked certain.
But, as is so often the case, the visitors capitalised on that let-off ruthlessly, going straight up the other end to force a Tagliafico own goal from a horribly miscued Sadio Mane shot that followed a sublime turn in the box.
The hosts responded well to that setback, and would have been level at the break had Fabinho not acrobatically cleared Dusan Tadic's lobbed attempt off the line with Adrian stranded.
That late scare and a general lack of control in the middle throughout prompted Jurgen Klopp to make a half-time change, with youngster Curtis Jones making way for captain Jordan Henderson.
But the substitution looked to have made little difference when Ajax danced their way through the Liverpool midfield before teeing up Klaassen to strike the post with a thunderous effort just over a minute after the restart.
With attempts to shore things up failing, Klopp instead opted to switch things up in attack, calling Diogo Jota, Takumi Minamino and Xherdan Shaqiri from the bench to replace his starting front three.
However, those changes only served to largely disrupt the flow of the game rather than add any thrust for the visitors, not that they would have minded.
Consequently, both sides struggled to create much during a scrappy finish to the game that ensured Liverpool took all three points.
What does it mean? Promising start for Reds
On paper, trips to Ajax and Atalanta looked like the toughest tests Liverpool would face as they plotted a route out of Group D.
To have got one of those fixtures out of the way with three points on the board represents an excellent start for Klopp's men, despite their failure to hit the heights in terms of performance.
Gomez shines in Van Dijk's absence
With Van Dijk likely out for the season following knee surgery, Liverpool desperately need his younger partner to step up and take on responsibility.
Gomez certainly looked ready to do that here as he won five aerial duels, made 10 clearances and regained possession on 11 separate occasions.
Jones struggles on European debut
Making his first appearance in the Champions League, Jones would have hoped to show more before being brought off at half-time.
The talented teenager had an 89 per cent passing accuracy, but struggled on the other side of the ball, making no tackles or interceptions and winning just 50 per cent of his duels.
Key Opta facts
- Liverpool are unbeaten in their last seven away trips against Dutch opponents, keeping a clean sheet in five of those encounters (winning four, drawing three).
- Ajax have won only one of their previous seven games against English opponents in European competition (D2 L4). That victory came in a Champions League semi-final first leg win over Tottenham in 2018-19.
- Tagliafico is the first Ajax player to score an own goal in the Champions League since Vurnon Anita against Real Madrid in September 2010.
- At 34 years and 291 days, James Milner became the third-oldest player to appear for Liverpool in the European Cup or Champions League, after Gary McAllister (37y 84d) and Ian Callaghan (35y 353d). In contrast, Jones was fifth-youngest Champions League outfield player to start for Liverpool (19y 265d).
Liverpool turn their attentions back to the Premier League with an Anfield clash against Sheffield United on Saturday, while Ajax travel to VVV Venlo.